A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ; Adapted to the Use of Students ; Extracted Mostly from Similar Works of Ludlam, Playfair, Vince, and Bonnycastle |
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Page xii
... manner which goes to the bottom of it , brings many curious properties to light , not observed by former writers , and clears up many difficulties . " * The learner will not be duly qualified to study this treatise with advantage , if ...
... manner which goes to the bottom of it , brings many curious properties to light , not observed by former writers , and clears up many difficulties . " * The learner will not be duly qualified to study this treatise with advantage , if ...
Page 3
... , abc any other angle , ab the radius ; then , in the same manner , the angle abc will vary as - ac at AC ac Hence the angle ABC angle abc :: AB ab TRIGONOMETRY . 8. TRIGONOMETRY is a branch of the general INTRODUCTION . 3.
... , abc any other angle , ab the radius ; then , in the same manner , the angle abc will vary as - ac at AC ac Hence the angle ABC angle abc :: AB ab TRIGONOMETRY . 8. TRIGONOMETRY is a branch of the general INTRODUCTION . 3.
Page 6
... the end of the quad- rant , in like manner as the tangent and secant are referred to the diameter AD passing through the beginning of the quad- rant . + It appears also , that the cosine , cotangent 6 PLANE TRIGONOMETRY .
... the end of the quad- rant , in like manner as the tangent and secant are referred to the diameter AD passing through the beginning of the quad- rant . + It appears also , that the cosine , cotangent 6 PLANE TRIGONOMETRY .
Page 8
... manner , Cf , the cosine of the arc AHb , is equal to CF , the cosine of the arc AB ; but is negative , because it falls on the other side of the centre C , whence the cosines have their origin . 36. Again , At the tangent , and Ct the ...
... manner , Cf , the cosine of the arc AHb , is equal to CF , the cosine of the arc AB ; but is negative , because it falls on the other side of the centre C , whence the cosines have their origin . 36. Again , At the tangent , and Ct the ...
Page 9
... t and c the tangent and cotangent of the second ; then T × C = radius ( 41 ) , and txc - radius2 ; therefore TxC = txc , there- fore Tt : c : C ( 16. 6 ) . B In the same manner it may be shown , that PLANE TRIGONOMETRY .
... t and c the tangent and cotangent of the second ; then T × C = radius ( 41 ) , and txc - radius2 ; therefore TxC = txc , there- fore Tt : c : C ( 16. 6 ) . B In the same manner it may be shown , that PLANE TRIGONOMETRY .
Common terms and phrases
90 degrees adjacent angle AHDL algebra analogy angle ABC angle ACB Answer arc or angle base centre chord circle comp complement cosecant cosine cotangent Euclid's Elements find the angles find the rest geometry Given the side greater than 90 half the sum half their difference height Hence hypothenuse AC included angle less than 90 logarithmic sines mathematics measured mechanical philosophy negative opposite angle perp perpendicular plane triangle plane trigonometry PROP propositions quadrant AH quantity right-angled spherical triangle right-angled triangle Scholium secant side AB side AC sides and angles sine a sine sine and cosine sine² sines and tangents solution spherical angle spherical triangle ABC spherical trigonometry supplement tables tangent of half theorems third side three angles three sides triangle are given trigono versed sine yards
Popular passages
Page 12 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page ix - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 23 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Page 13 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.
Page 87 - The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The sine of half the sum of two sides of a spherical...
Page 74 - The sum of any two sides is greater than the third side, and their difference is less than the third side.